Nonlinear phase-shift compensation method and apparatus

ABSTRACT

A nonlinear phase-shift compensation method and apparatus is provided for improving system performance in optical transmission systems. The apparatus includes a phase-shift compensating device that provides a partial compensating phase shift to reduce the nonlinear phase noise resulting from self-phase modulation and amplified spontaneous emissions in an optical transmission system.

FIELD OF INVENTION

[0001] This invention relates generally to the field of opticaltelecommunications, and in particular, to a method and apparatus forimproving optical transmission performance by reducing phase jitter inoptical transmission systems using a nonlinear phase-shift compensator.

BACKGROUND OF THE INVENTION

[0002] Ultra-long-haul (ULH) optical transmission is of crucialimportance to increase the flexibility of future optical networks. Thetransmission distance of ULH transmission is limited by amplifiedspontaneous emission (ASE) noise and fiber nonlinearities. The use ofdispersion-managed solitons (DMS) and other signal formats in suchsystems has attracted attention because of the potential for increasedtransmission performance. DMS systems balance self-phase-modulation(SPM) with fiber dispersion, and avoid intra-channelcross-phase-modulation (XPM) and four-wave-mixing (FWM) by maintaining amoderate degree of pulse breathing. However, there exists a severenonlinear penalty in DMS-based dense-wavelength-multiplexed (DWDM)transmissions, namely inter-channel XPM which introduces severe timingjitter.

[0003] Differential-phase-shift-keying (DPSK) and other phase-shiftkeying modulation formats such as quadrature phase-shift keying (DQPSK)have also attracted much attention because of their potential tosignificantly reduce the XPM penalty in DWDM systems. However, theperformance of such systems is generally limited by theGordon-Mollenauer effect, in which ASE power noise is converted intophase noise by self-phase modulation (SPM).

[0004] Nonlinearity management based on distributed nonlinearitycompensation (nonlinearity compensated at several locations within asoliton period) has been proposed to improve transmission performance. Adistributed nonlinear compensator is, however, extremely complicated,and therefore very expensive. An example of distributed nonlinearitycompensation includes fibers with alternating positive and negativenonlinear refractive indices (n2). Such fibers can be used toeffectively cancel the nonlinear phase shift resulting from SPM.However, such fiber does not exist at the communication wavelengthwindow (˜1.55 um). Accordingly, a need exists for a practical and costeffective method and apparatus for reducing the nonlinear phase noiseresulting from SPM and ASE.

SUMMARY OF THE INVENTION

[0005] In accordance with one aspect of the invention, nonlinear phaseshift compensation is provided for improving system performance ofoptical transmissions by reducing the nonlinear phase noise resultingfrom SPM and ASE. In one embodiment of the method and apparatus of theinvention, nonlinear phase noise in PSK systems, induced by SPM, isreduced by adding a phase shift proportional to the pulse power of eachoptical pulse.

[0006] In a preferred embodiment of the invention, quadratic nonlinearmaterials are provided, such as periodically-poled LiNbO3 (PPLN), togenerate the nonlinear phase shifting needed in NPSC.

[0007] In another embodiment, a phase modulator is used to modulate thephase of the data pulses that are to be applied to a PSK receiver. Thephase modulation is data driven such that the magnitude of the phasemodulation introduced in the phase modulator is arranged to beproportional to the detected data pulse intensity, while the sign isarranged to be opposite to the nonlinear phase shift caused by SPM.

[0008] Significant performance improvement is achieved by such NPSCdevices in single-channel and WDM transmission systems.

BRIEF DESCRIPTION OF THE DRAWINGS

[0009] The present invention will be more fully appreciated byconsideration of the following detailed description, which should beread in light of the drawings in which:

[0010]FIG. 1 is a schematic diagram of a DPSK system according to oneembodiment of the invention;

[0011]FIG. 2 is a schematic diagram of one embodiment of an NPSCapparatus of the invention;

[0012]FIGS. 3a-c are phasor diagrams of the optical field forsingle-channel, 100 GHz spaced WDM, and 50 GHz spaced WDM transmissionsin a DMS-DPSK system, without NPSC, respectively;

[0013]FIGS. 3d-f are phasor diagrams of the optical field forsingle-channel, 100 GHz spaced WDM, and 50 GHz spaced WDM transmissionsin a DMS-DPSK system, with NPSC, respectively;

[0014]FIG. 4 is a diagram illustrating the dependence of differentialphase Q factor on the amount of compensating nonlinear phase shift insingle-channel system (circles) and DWDM systems with 100-GHz (squares)and 50-GHz (diamonds) channels spacings;

[0015]FIG. 5 is a schematic drawing of another embodiment of an NPSCapparatus according to the invention for a DPSK system withpost-nonlinearity compensation based on data-driven phase modulation;

[0016]FIGS. 6a-b are eye-diagrams after transmission over a distance of6000 km without and with data-driven phase modulation based post NPSC,respectively;

[0017]FIG. 7 shows plots of Q-factors vs. transmission distance for aWDM system with and without NPSC; and

[0018]FIG. 8 is a plot showing the improvement of phase-Q at atransmission distance of 6000 km as a function of the effectiveelectrical bandwidth.

DETAILED DESCRIPTION OF THE INVENTION

[0019] A schematic diagram of a DMS-DPSK system 10 according to oneembodiment of the invention is shown in FIG. 1. One the transmitterside, a DBF laser 20 and a pulse generator 22 are used to generate apulse train (e.g., with a repetition rate of 10 GHz and a duty cycle of33% (pulse full width half maximum (FWHM) of 33 ps)). A 10 Gb/sdifferential data encoder 25 and a phase modulator 26 are provided toencode data from data source 27 in the phase of the optical pulses insuch a way that every 0(1) in the original data is represented by a π(0)shift in the relative phase of two adjacent pulses. A multiplexer 30 isused to multiplex several WDM channels before being launched into adispersion-managed link 35.

[0020] On the receiver side, the WDM channels are de-multiplexed using ademultiplexer 50. A polarization controller 55, which may comprise threewaveplates, is preferably used to rotate the polarization of the signalwave such that the signal output polarization matches well with thedesired direction of the NPSC device 60 to maximize the efficiency ofnegative nonlinear phase shift generation.

[0021] Each channel is then sent through an NPSC device 60 that providesa partial compensating nonlinear phase shift to reduce to nonlinearphase noise from SPM and ASE. The compensating phase shift isapproximately proportional to the pulse power of the optical pulsestransmitted by the system 10. The partial compensating phase shift iseffectively provided over a central portion of the bit period oftransmitted pulses (i.e. within the decision window of each bit slot)and compensates for only a portion of the magnitude of the phase shiftresulting from SPM and ASE.

[0022] Specifically, the partial compensating phase shift does notprovide a compensating phase shift (to eliminate nonlinear phase noise)for a transmitted pulse outside of the decision window of each bit slot(e.g. outside of the central 20% of the bit period). Further, themagnitude of the partial compensating phase shift is not equal to themagnitude of the phase shift resulting from SPM and ASE. The partialcompensating phase shift is, however, sufficient to substantiallyeliminate nonlinear phase noise which results from SPM and ASE.

[0023] Each channel is then decoded at a DPSK receiver 65. The DPSKreceiver 65 preferably comprises a differential phase decoder thatincludes an optical delay interferometer and a balanced detector (notshown).

[0024] Lumped NPSC can be performed either at the receiver 65, or atother locations along a dispersion managed link. Lumped NPSC providessignificant Q factor improvement (e.g., greater than about 3 dB) inultra-long-haul DMS-DPSK systems, even when many wavelength channels areclosely multiplexed. For DWDM systems with bit rates of 10 Gb/s perchannel a transmission distance of about 6,000 km or more can beachieved.

[0025] The following table shows the number of compensators (N), therespective approximate location for the compensators along the length(L) of the dispersion managed link 35, and the normalized phase shiftfactor, and the reduction in nonlinear phase noise variance for systemshaving 1 to N compensators. Normalized Reduction in phase nonlinearNumber of shift phase noise compensators Location(s) factor variance 1 L−1/2  6 2 L/2, L −1/2, −1/4 12 3 L/3, 2L/3, L −1/3, −1/3, −1/6 15.6 . .. . . . . . . . . . N L/N, 2L/N, . . . −1/N, −1/N . . . 1/N, 20log(2N)(N − 1)L/N, L −1/2N

[0026] The normalized phase shift factor is multiplied by the peak pulsephase shift, after transmission through the system, to determine anoptimum phase shift for each transmitted pulse. It can be appreciated bythose skilled in the art that the location(s) of the compensators can bevaried by about 50%, and the normalized phase shift factor(s) can bevaried by about 70% while still providing a significant improvement intransmission performance.

[0027] In a preferred embodiment, the NPSC device 60 is aperiodically-poled waveguide 210. As shown in FIG. 2, the waveguide 210is preferably a LiNbO₃ (PPLN) waveguide in which negative nonlinearphase shifts in excess of about 1 rad can be produced with realisticpump powers by a cascaded χ⁽²⁾:χ⁽²⁾ process.

[0028] A cascade quadratic process is basically a phase-mismatchedsecond-harmonic generation process that effectively generates onto theincoming pulse a phase shift that is approximately proportional to theintensity of the pulse. The sign of the generated nonlinear phase shiftis determined by the sign of the phase-mismatch that is related to thedifference between the indexes of reflection of the signal wave and itssecond harmonic. The magnitude of the generated phase shift isapproximately inversely proportional to the degree of the phase-mismatchand signal power, both of which can be controlled/varied to obtain anoptimum nonlinear phase shift desired for the reduction of signal phasenoise.

[0029] The phase-mismatch can be controlled by changing the temperatureof the PPLN waveguide 210 using, for example, temperature controller220. Assuming realistic PPLN waveguide parameters and a phase mismatchof ˜4π, the effective nonlinear coefficient of the PPLN waveguide 210 isapproximately 10⁴ times that of silica fiber. The estimated powerrequirement for compensating the nonlinear phase shift associated with6,000 km of DMS transmission is less than about 100 mW. The bandwidth ofthe NLPC device 60 is about 0.3 nm, which is adequate for applicationsin conventional 10-Gbit/s DMS systems. The temperature controller 220 isused to control the temperature of the PPLN waveguide 210 to the valuethat gives the appropriate sign of phase-mismatch, and thus theappropriate sign of nonlinear phase shift, and the appropriate magnitudeof the phase shift. An optical amplifier 230 is preferably used to boostthe power of the received signal so that the nonlinear phase shiftgenerated by PPLN waveguide 210 is substantially an optimum value forreducing the phase noise. As discussed above with reference to thetable, the location(s) of the compensator(s) can be varied by about 50%,and the normalized phase shift factor(s) can be varied by about 70%while still providing a significant improvement in transmissionperformance.

[0030] Numerical simulations were performed to verify the effectivenessof NPSC. DMS-DPSK transmission was modeled with five 10-Gbit/s WDMchannels, each of which is modulated by a 2⁷−1 pseudo-random binarysequence, sufficient to take into consideration the intra-channelpattern dependence with the dispersion map used in the simulation.Normally, in DMS systems, only the adjacent bits interact with eachother, and the interaction is very weak since solitons maintainwell-defined temporal profiles during propagation in fiber links,therefore 2⁷−1 pseudo-random binary sequence is sufficient to take intoconsideration the intra-channel pattern dependence.

[0031] As shown in FIG. 1, the dispersion-managed link 35 of the DPSKsystem 10 comprises a pre-dispersion fiber 36, one or more dispersionmanaged spans 47, each followed by a post-dispersion fiber 45. Eachdispersion managed span 47 comprises a 100-km fiber span 42, (D=6ps/km/nm), an amplifier and a dispersion-compensating fiber 43 (DCF).

[0032] The pre-dispersion is −300 ps/nm and the post-dispersion is fixedat 150 ps/nm. The dispersion of each fiber span 42 is partiallycompensated by the DCF 43. The residual dispersion per dispersionmanaged span 47 is about 10 ps/nm. The nonlinear coefficient is 1.8W/km. Fiber loss is about 23 dB per 100-km fiber span 42, and iscompensated by backward Raman amplification. The path-average signalpower is about −8 dBm per channel and the ASE noise level is about −36dB per fiber span 42 (the ASE noise is defined as the added noise powerin a bandwidth of 0.1 nm, measured relative to the signal power).

[0033]FIGS. 3a-f show the phasor diagrams of the centers of outputpulses after 6,000 km of transmission in 10-Gbit/s modeled DMS-DPSKsystems. The phasor diagrams show the electrical fields of the bits in apolar coordinate to clearly illustrate the variance due to amplitudejitter and phase jitter. FIGS. 3a and 3 d pertain to a single-channelsystem, without and with NPSC, respectively. The mean phase shift fromSPM (observed in a noiseless simulation) is ˜3.1 rad. There is also aphase shift of ˜0.3 rad from XPM between ASE noise (in the entiresimulation window) and the signal.

[0034] The mean compensating phase shifts was set to be −1.4 rad. Thetotal phase variance was reduced by 5.2 dB. FIGS. 3b and c, and 3 e andf pertain to a WDM system with a channel spacing of 100 and 50 GHz,without (b and c) and with (e and f) NPSC, respectively. The meancompensating phase shifts are the same as those used in FIG. 3d. Themean signal phase shift is ˜1.2 rad larger in both five-channel casesthan in the single-channel case, owing to inter-channel XPM. Even whenthe channel spacing is reduced to 50-GHz, the proposed NPSC scheme isstill very effective. The Q-factor can be improved by approximately 4 dBor more through NPSC. The slight reduction of effectiveness when channelspacing is reduced is due to the fact that the nonlinear phase noiseresulting from XPM and ASE induced amplitude fluctuations, which can notbe reduced by NPSC, is enhanced with the reduction of channel spacing.

[0035] To find the substantially maximal performance improvementobtained by NPSC and to find the optimal compensating phase shift, thedifferential phase Q factors (defined as 7 r divided by the sum of theRMS variations of differential phases between two adjacent bits around1s and 0s) were calculated for several values of the compensating phaseshift. The data (128 bits per channel) was propagated through the samelink 64 times with different ASE noises and the phase noise variance wascalculated after each transmission with different compensating nonlinearphase shifts. FIG. 4 shows the dependence of Q² (in dB) on thecompensating phase shift in a single-channel system 410 and WDM systemswith 100-GHz 420 and 50-GHz 430 channel spacings. In all three cases, asubstantially optimal compensating phase shift is approximately −1.5rad., which is close to one-half of the accumulated nonlinear phaseshift. Under substantially optimal NPSC, the phase noise variance, whichis inversely proportional to Q², is reduced by 5.2 dB, 4.8 dB, and 3.6dB in the three transmission configurations, respectively.

[0036] Phase jitter was also simulated in single-channel and WDM systemswith NPSC at the middle and end points of the system. As discussed aboveand shown in the above table, the combination of interior and end pointNPSC devices produced a larger reduction in phase jitter than an endpoint NPSC device alone.

[0037] In another preferred embodiment of an NPSC device 500 accordingto the invention, as shown in FIG. 5, an optical phase modulator 510 isprovided, which is used to modulate the phase of the data pulses infront of a receiver (not shown). The nonlinear phase noise is preferablycompensated within the decision window of each bit slot (e.g., thecentral 20% of the bit period), to make NPSC much more practical. Themagnitude of the phase modulation is preferably directly proportional tothe detected pulse intensity, and the sign is opposite to the nonlinearphase shift caused by SPM. Thus, the nonlinear phase noise induced byamplitude fluctuation and SPM in the central window of each bit periodis substantially compensated.

[0038] To obtain a substantially optimum transmission performance, themagnitude and sign of the phase modulation (i.e. the normalized phaseshift factor) is preferably provided as discussed above with referenceto the table. As also discussed above, the location(s) of thecompensator(s) can be varied by about 50%, and the normalized phaseshift factor(s) can be varied by about 70% while still providing asignificant improvement in transmission performance.

[0039] To avoid potential bandwidth limitations and peak powerrequirements of nonlinear crystals, the embodiment shown in FIG. 5 usesa data-driven phase modulator 510 to generate, in effect, negativenonlinear phase shift. As shown in FIG. 5, a PIN-diode 520 may be usedto detect the incoming data stream 530. The PIN-diode 520 preferably hasan FWHM electrical bandwidth of about 10 GHz. The output of thePIN-diode 540 is used to drive the phase modulator 510 with anelectrical bandwidth of about 10 GHz. A variable RF delay line 550 ispreferably used so that the optical and electrical signals of the samedata pulse arrive simultaneously at the phase modulator 510. Preferably,the sign of the drive voltage is such that the phase modulationgenerated by the phase modulator 510 is the opposite of that generatedby SPM.

[0040] Polarization diversity schemes, including the use of a pluralityof phase modulators 510, may also be incorporated if the phasemodulator(s) 510 are polarization sensitive. An RF amplifier 560 ispreferably used to boost the amplitude of the RF signal so that theresulting phase shift is close an optimum value for NPSC.

[0041] It can be understood by a person skilled in the art that aplurality of NPSC devices 60 according to the invention may be employedin a WDM optical transmission system over multiple dispersion managedspans 47 to reduce phase jitter on a plurality of channels of a WDMsystem.

[0042] The transmitted eye-diagram for a system employing an NPSC deviceas shown in FIG. 1 is shown in FIG. 6. Eye-diagrams provide a goodpicture of how well a certain transmission system is performing. Thewider the eye-opening, the better the performance of the receivedsignal. It is evident from FIG. 6 that, with NPSC, the eye-opening ismuch wider than without NPSC.

[0043] The system Q factor as a function of transmission distance isshown in FIG. 7. Q-factor is directly related the bit-error-rate ofreceived signals. At a Q-factor value of 15.5 dB, the correspondingbite-error-rate is ˜10⁻⁹, which is commonly referred to as theerror-free requirement. As can be seen from FIGS. 6 and 7, reducingphase jitter by NPSC significantly improves the performance of aDMS-DPSK system.

[0044] As can be seen from FIG. 8, NPSC devices with ultra-fast responseare not necessary in nonlinearity management. The effective electricalbandwidth of the phase modulation of the present invention, (i.e., theelectrical bandwidth of the PIN-diode 520, the RF amplifier 560, and thephase modulator 510 combined), is preferably greater than about 4 GHz(or about 40% of the line rate) in order to obtain the full benefit ofNPSC. Therefore, the bandwidth of line rate components is more thansufficient for NPSC. In addition, the optimum value for the NPSC isapproximately half the total accumulated nonlinear phase shift, which istypically much less than π in an ULH DWDM system. Thus, the method ofthe present invention can be readily implemented in 40 Gb/s DPSK systemsand beyond.

[0045] Phase modulators 510, such as Lithium Niobate modulators, arealso applicable in broad wavelength range, which makes embodiments ofthe present invention very attractive in broadband DWDM transmissionsystems.

[0046] It will be appreciated by those skilled in the art that variouschanges can be made to the embodiments described above without departingfrom the broad inventive concept thereof. It is understood, therefore,that this invention is not limited to the particular embodimentsdisclosed, but is intended to cover modifications within the spirit andscope of the appended claims and their legal equivalents. For example,although some of the embodiments disclosed herein have been describedwith reference to DMS-DPSK signal/modulation formats, other signalformats, such as NRZ and RZ, and other modulation formats, such as ASK,PSK, DPSK and DQPSK, may be employed with the apparatus and method ofthe invention.

1. A phase-shift compensator apparatus comprising: one or morephase-shift compensating devices, wherein the one or more phase-shiftcompensating devices provide a partial compensating phase shift toreduce the nonlinear phase noise resulting from self-phase modulationand amplified spontaneous emissions in an optical transmission system.2. The apparatus of claim 1 wherein the partial compensating phase shiftis effectively provided over a central portion of the bit period oftransmitted pulses.
 3. The apparatus of claim 1 wherein the partialcompensating phase shift compensates for only a portion of the magnitudeof the phase shift of a transmitted pulse resulting from SPM and ASE. 4.The apparatus of claim 1, wherein the phase-shift compensating deviceincludes quadratic nonlinear material with an effective nonlinear indexof refraction n₂<0 from the cascaded χ⁽²⁾:χ⁽²⁾ effect.
 5. The apparatusof claim 4, wherein the quadratic nonlinear material includesperiodically-poled LiNbO3.
 6. The apparatus of claim 1, wherein the oneor more phase-shift compensating devices include at least one phasemodulator.
 7. The apparatus of claim 6, further comprising drive meansfor driving the phase modulator such that the magnitude of the phasemodulation is proportional to input data pulse intensity, and the signof the phase shift is opposite to the phase shift caused by self-phasemodulation.
 8. The apparatus of claim 7, wherein the drive meansincludes: a PIN diode; an RF amplfier; and a variable RF delay.
 9. Theapparatus of claim 1 wherein the one or more phase-shift compensatingdevices are adapted to provide compensation in an optical communicationsystem employing a return-to-zero signal format.
 10. The apparatus ofclaim 1 wherein the one or more phase-shift compensating devices areadapted to provide compensation in an optical communication systememploying a non-return-to-zero signal format.
 11. The apparatus of claim1 wherein the one or more phase-shift compensating devices are adaptedto provide compensation in an optical communication system employing adispersion managed soliton signal format.
 12. The apparatus of claim 1wherein the one or more phase-shift compensating devices are adapted toprovide compensation in an optical communication system employing anamplitude-shift keying modulation format.
 13. The apparatus of claim 1wherein the one or more phase-shift compensating devices are adapted toprovide compensation in an optical communication system employing aphase-shift keying modulation format.
 14. The apparatus of claim 13wherein the phase-shift keying modulation format is a differentialphase-shift keying modulation format.
 15. The apparatus of claim 13wherein the phase-shift keying modulation format is a differentialquadrature phase-shift keying modulation format.
 16. A phase-shiftcompensator apparatus comprising: one or more phase-shift compensatingdevices, wherein the one or more phase-shift compensating devices areprovided along the length L of a transmission system and provide acompensating phase shift according to the following table NormalizedPhase Compensators Location Shift Factor 1 L −1/2 2 L/2, L −1/2, −1/4 3L/3, 2L/3, L −1/3, −1/3, −1/6 . . . . . . . . . N L/N, 2L/N, . . . (N −1)L/N, L −1/N, −1/N, . . . −1/N, −1/2N

wherein the normalized phase shift factor is multiplied by the peakpulse phase shift after transmission through the transmission system todetermine an optimum compensating phase shift.
 17. The apparatus ofclaim 16 wherein the location of the compensator(s) can be varied byabout 50% while providing a compensating phase shift and improvedtransmission performance.
 18. The apparatus of claim 16 wherein thenormalized phase shift factor can be varied by about 70% while providinga compensating phase shift and improved transmission performance. 19.The apparatus of claim 16, wherein the one or more phase-shiftcompensating devices include quadratic nonlinear material with aneffective nonlinear index of refraction n₂<0 from the cascaded χ⁽²⁾:χ⁽²⁾effect.
 20. The apparatus of claim 19, wherein the quadratic nonlinearmaterial includes periodically-poled LiNbO3.
 21. The apparatus of claim16, wherein the one or more phase-shift compensating devices include aphase modulator.
 22. The apparatus of claim 21, further comprising drivemeans for driving the phase modulator such that the magnitude of thephase modulation is proportional to input data pulse intensity, and thesign of the phase shift is opposite to the phase shift caused byself-phase modulation.
 23. The apparatus of claim 22, wherein the drivemeans includes: a PIN diode; an RF amplfier; and a variable RF delay.24. A phase-shift compensator apparatus comprising: one or morephase-shift compensating devices including: an optical amplifier; aperiodically-poled quadratic nonlinear waveguide coupled to theamplifier; a polarization controller for aligning pulse signalpolarization with an axis of the quadratic nonlinear waveguide; and atemperature controller for controlling the temperature of the quadraticnonlinear waveguide; wherein the one or more phase-shift compensatingdevices provide a partial compensating phase shift to reduce thenonlinear phase noise resulting from self-phase modulation and amplifiedspontaneous emissions in an optical transmission system.
 25. An opticalcommunication system comprising: a transmitter; a receiver; a dispersionmanaged link extending between the transmitter and the receiver; and oneor more phase-shift compensating devices provided along the dispersionmanaged link for providing a partial phase shift to transmitted pulsesto compensate for the nonlinear phase noise in the optical communicationsystem resulting from self-phase modulation and amplified spontaneousemissions.
 26. A method for nonlinear phase shift compensationcomprising: providing one or more phase-shift compensating devices alonga length L of an optical transmission system to provide a compensatingphase shift to input data pulses according to the following tableNormalized Phase Compensators Location Shift Factor 1 L −1/2 2 L/2, L−1/2, −1/4 3 L/3, 2L/3, L −1/3, −1/3, −1/6 . . . . . . . . . N L/N,2L/N, . . . (N − 1)L/N, L −1/N, −1/N, . . . −1/N, −1/2N

wherein the normalized phase shift factor is multiplied by the peakpulse phase shift after transmission through the transmission system todetermine an optimum compensating phase shift.
 27. The apparatus ofclaim 26 wherein the location of the compensator(s) can be varied byabout 50% while providing a compensating phase shift and improvedtransmission performance.
 28. The apparatus of claim 26 wherein thenormalized phase shift factor can be varied by about 70% while providinga compensating phase shift and improved transmission performance. 29.The method of claim 26, wherein the one or more phase-shift compensatingdevices include quadratic nonlinear material with an effective nonlinearindex of refraction n₂<0 from the cascaded χ⁽²⁾:χ⁽²⁾ effect.
 30. Themethod of claim 26, wherein one or more phase-shift compensating devicescomprises a phase modulator, and wherein the method further comprises:driving the phase modulator in synchronism with the input data pulsessuch that the magnitude of the phase modulation is proportional to inputdata pulse intensity, and the sign of the phase shift is opposite to thephase shift caused by self-phase modulation.
 31. A phase-shiftcompensator comprising: one or more phase-shift compensating means,wherein the one or more phase-shift compensating means provide a partialcompensating phase shift to reduce the nonlinear phase noise resultingfrom self-phase modulation and amplified spontaneous emissions in anoptical transmission system.
 32. A phase-shift compensator apparatuscomprising: one or more phase-shift compensating means, wherein the oneor more phase-shift compensating means are provided along the length Lof a transmission system and provide a compensating phase shiftaccording to the following table Normalized Phase Compensators LocationShift Factor 1 L −1/2 2 L/2, L −1/2, −1/4 3 L/3, 2L/3, L −1/3, −1/3,−1/6 . . . . . . . . . N L/N, 2L/N, . . . (N − 1)L/N, L −1/N, −1/N, . .. −1/N, −1/2N.


33. The apparatus of claim 32 wherein the location of the compensator(s)can be varied by about 50% while providing a compensating phase shiftand improved transmission performance.
 34. The apparatus of claim 32wherein the normalized phase shift factor can be varied by about 70%while providing a compensating phase shift and improved transmissionperformance.